Stetson
A Stetson was a hat, typically found in the western United States. The 1,103-year-old Eleventh Doctor donned a Stetson given to him by Craig Owens, (DW: Closing Time) while in Utah. When Rory complimented him on it, he replied, "It's a Stetson. I wear a Stetson now. Stetsons are cool" and the Stetson is promptly shot off his head by River Song, who had appeared behind him, echoing a previous incident with a fez. The current wearabouts of the Stetson are unknown. it was probably blown into the desert by the gun. (DW: The Impossible Astronaut).
In the Stetson's own timeline, it was given to the Doctor by Craig in episode 12, and the Doctor wears it through episodes 13 and 1. According to Craig, it's "From Sean's stag". Apparently, stag is short for stag party, the British name for a bachelor party.